Question

For IR radiation with û = 1,130 cm 1, v=__THz

Answer 1

Answer: The frequency of the radiation is 33.9 THz

Explanation:

We are given:

Wave number of the radiation, $\bar{\nu}=1130cm^{-1}$

Wave number is defined as the number of wavelengths per unit length.

Mathematically,

$\bar{\nu}=\frac{1}{\lambda}$

where,

$\bar{\nu}$ = wave number = $1130cm^{-1}$

$\lambda$ = wavelength of the radiation = ?

Putting values in above equation, we get:

$1130cm^{-1}=\farc{1}{\lambda}\\\\\lambda=\frac{1}{1130cm^{-1}}=8.850\times 10^{-4}cm$

Converting this into meters, we use the conversion factor:

1 m = 100 cm

So, $8.850\times 10^{-4}cm=8.850\times 10^{-4}\times 10^{-2}=8.850\times 10^{-6}m$

• The relation between frequency and wavelength is given as:

$\nu=\frac{c}{\lambda}$

where,

c = the speed of light = $3\times 10^8m/s$

$\nu$ = frequency of the radiation = ?

Putting values in above equation, we get:

$\nu=\frac{3\times 10^8m/s}{8.850\times 10^{-4}m}$

$\nu=0.339\times 10^{14}Hz$

Converting this into tera Hertz, we use the conversion factor:

$1THz=1\times 10^{12}Hz$

So, $0.339\times 10^{14}Hz\times \frac{1THz}{1\times 10^{12}Hz}=33.9THz$

Hence, the frequency of the radiation is 33.9 THz